Summary
The matrix of fundamental solutions is constructed and used to obtain an integral representation for the displacement vector of the field equations of linear couple stress theory. The dynamic volume potential and single and double layer surface potentials are defined and the analogue of Poisson formula is obtained. The formal solutions to two fundamental boundary value problems are expressed by integral representations involving Green's matrices.
Zusammenfassung
Die Matrix der Fundamentallösungen wird hergeleitet und zur Angabe einer Integraldarstellung des Verschiebungsvektors und der Feldgleichungen der linearen Momentenspannungstheorie verwendet. Das dynamische Volumspotential sowie die Oberflächenpotentiale der einfachen und der Doppelschicht werden definiert und das Analogon zur Poissonschen Formel erhalten. Formale Lösungen von zwei Randwertproblemen werden in Form von Greensche Matrizen enthaltenden Integraldarstellungen angegeben.
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Dhaliwal, R.S., Chowdhury, K.L. Potential methods in the linear couple-stress theory of elasticity. Acta Mechanica 15, 165–176 (1972). https://doi.org/10.1007/BF01304290
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DOI: https://doi.org/10.1007/BF01304290